The incompleteness property says that there are infinitely many martingale
measures producing an interval of arbitrage-free prices. In reality one has to
charge a reasonable price for partial hedging (not for total hedging) of the risks and bear some residual risk, which implies selecting an equivalent martingale measure (EMM) based on some 'optimality' concept.
I'll include Cont and Tankov view from 'Financial Modeling with Levy Processes' and 'Financial Modeling with Jump Processes'.
(Chapter 10 in the second reference) "In a complete market, there is only one arbitrage-free way to value an
option: the value is defined as the cost of replicating it. In real markets, as
well as in the models considered in this book, perfect hedges do not exist and
options are not redundant: the notion of pricing by replication falls apart, not
because continuous time trading is impossible in practice but because there
are risks that one cannot hedge even by continuous time trading. Thus we
are forced to reconsider hedging in the more realistic sense of approximating
a target payoff with a trading strategy: one has to recognize that option
hedging is a risky affair, specify a way to measure this risk and then try to
minimize it. Different ways to measure risk thus lead to different approaches
to hedging: superhedging, utility maximization and mean-variance hedging
are among the approaches discussed in this chapter. Each of these hedging
strategies has a cost, which can be computed in some cases. The value of the
option will thus consist of two parts: the cost of the hedging strategy plus a
risk premium, required by the option seller to cover her residual (unhedgeable)
risk. We will deal here with the first component by studying various methods
for hedging and their associated costs. Arbitrage pricing has nothing to say
about the second component which depends on the preferences of investors
and, in a competitive options market, this risk premium can be driven to zero,
especially for vanilla options."
@river_rat mentions here (in the comments), in the context of Heston market price of volatility risk, that the extra EMM parameter could (should) be used "in the stability of the resulting hedge ratios (which is sadly usually of secondary concern)".